Solving Bu Siska's Fruit Purchase: A Math Adventure

Hey guys, let's dive into a fun math problem! We're going to help Bu Siska figure out the best way to spend her money on fruits. This is a classic example of a linear programming problem, where we're trying to optimize something (in this case, the amount of fruit she can buy) while staying within certain constraints (her budget and the capacity of her vehicle). So, grab your calculators (or your brains!) because we're about to put on our thinking caps. This type of problem is super practical; it's the kind of thing that comes up when you're planning a trip, budgeting for groceries, or even deciding how to allocate resources in a business. Let's break down the details, understand the problem step-by-step, and arrive at a solution. This will provide you with a solid foundation for tackling similar optimization challenges in the future. We'll start with the problem statement and then move on to the solution using clear explanations.

Understanding the Problem: Bu Siska's Fruit Shopping

Okay, so here's the deal: Bu Siska wants to buy some fruits. She loves oranges, which cost Rp 12,000 per kg, and apples, which go for Rp 15,000 per kg. She has a budget of Rp 600,000 to spend. Moreover, her vehicle can carry a maximum of 60 kg of fruit. But, here's the twist: she must buy 30 kg of oranges. The main questions here are:

• How many apples can Bu Siska buy?
• How much money will Bu Siska spend?

This kind of situation pops up all the time. Imagine you're planning a party. You have a certain budget, and you need to figure out how many snacks and drinks you can buy. Or, think about a business owner deciding how much of different products to order based on their budget and storage space. It is a very applicable scenario. We're going to break it down. We'll use our knowledge of inequalities and a bit of algebraic thinking to solve this. It's like a puzzle, and it's super rewarding to see the pieces come together to create a solution. The best part is, once you understand the basic principles, you can apply them to all sorts of real-life situations. So, let's roll up our sleeves and get started!

Defining Variables and Constraints

First things first, let's define our variables. This helps us translate the word problem into a mathematical language we can work with. Let:

• x = the number of kilograms of oranges Bu Siska buys.
• y = the number of kilograms of apples Bu Siska buys.

Now, let's write down the constraints. These are the limitations that Bu Siska has to work within:

1. Budget Constraint: The total cost of the oranges and apples must be less than or equal to her budget of Rp 600,000. This translates to the inequality: 12000x + 15000y ≤ 600000
2. Capacity Constraint: The total weight of oranges and apples cannot exceed the vehicle's capacity of 60 kg. This gives us: x + y ≤ 60
3. Minimum Orange Requirement: Bu Siska must buy at least 30 kg of oranges. So, x = 30
4. Non-negativity Constraint: Bu Siska cannot buy a negative amount of fruits. Thus, x ≥ 0 and y ≥ 0

See how we've taken the word problem and transformed it into a set of equations and inequalities? This is crucial. It gives us a structured way to solve the problem. Also, this approach makes it easier to understand and apply. For example, the budget constraint ensures that Bu Siska doesn't overspend. The capacity constraint makes sure she doesn't overload her vehicle, and the minimum orange requirement, well, ensures she gets her oranges! It is all very important to establish a foundation for more complex real-world situations.

Solving for the Number of Apples

Since Bu Siska must buy 30 kg of oranges, we know that x = 30. We can now use this information along with the constraints to find out how many apples she can buy.

First, let's use the budget constraint: 12000x + 15000y ≤ 600000. Substitute x = 30:

12000(30) + 15000y ≤ 600000 360000 + 15000y ≤ 600000 15000y ≤ 240000 y ≤ 16

Next, let's look at the capacity constraint: x + y ≤ 60. Substitute x = 30:

30 + y ≤ 60 y ≤ 30

So, from the budget constraint, Bu Siska can buy at most 16 kg of apples. From the capacity constraint, she can buy at most 30 kg of apples. Because the budget constraint is more restrictive, the maximum amount of apples she can buy is 16 kg. Therefore, based on her constraints, the maximum number of apples Bu Siska can buy is 16 kg.

Calculating the Total Spending

Now that we know Bu Siska will buy 30 kg of oranges and 16 kg of apples, let's calculate her total spending:

Cost of oranges: 30 kg * Rp 12,000/kg = Rp 360,000 Cost of apples: 16 kg * Rp 15,000/kg = Rp 240,000

Total spending: Rp 360,000 + Rp 240,000 = Rp 600,000

This means that Bu Siska will spend her entire budget, exactly Rp 600,000. It's a perfect fit! This outcome is a classic example of how to make the best use of a limited budget. It is a good lesson for personal finance. This is why having knowledge of these principles is important for effective financial planning. Understanding these types of calculations enables informed decision-making.

Conclusion: The Fruitful Outcome

So, the solution is:

• Bu Siska can buy 16 kg of apples.
• Bu Siska will spend a total of Rp 600,000.

It is important to understand that the model and solution are designed to provide the most optimal outcome within the given parameters. The same principles can be applied to many different real-world scenarios. We successfully used the constraints to figure out the best shopping plan. She gets her oranges, and she maximizes the amount of fruit she can buy while staying within her budget and vehicle's capacity. Isn't it cool how math can help us make smart choices? This is not just about solving a problem; it's about understanding how to optimize resources. And that, my friends, is a super valuable skill, no matter what you do in life. Keep practicing these types of problems, and you'll become a whiz at making the most of what you have! It's all about logical thinking and the ability to break down complex situations into simpler parts. This is a great starting point for more complex math challenges.